Fluctuation Correction and Global Solutions for the Stochastic Shigesada-Kawasaki-Teramoto System via Entropy-Based Regularization

TL;DR

This paper introduces a noise correction for the stochastic SKT system, proving the existence of global solutions using entropy-based regularization, advancing understanding of stochastic population models.

Contribution

It develops an entropy-based regularization method to establish global solutions for the stochastic SKT system, incorporating fluctuation corrections.

Findings

Existence of nonnegative, global, weak martingale solutions.

Development of a noise term based on particle system approximation.

Application of entropy structure for regularization.

Abstract

We derive a noise term to account for fluctuation corrections based on the particle system approximation for the n-species Shigesada-Kawasaki-Teramoto (SKT) system. For the resulting system of stochastic partial differential equations (SPDEs), we establish the existence of nonnegative, global, weak martingale solutions. Our approach utilizes the regularization technique, which is grounded in the entropy structure of the system.